Conventionally, a helical-gear positive displacement flowmeter is characterized in that the flow meter generates a very small amount of vibrations and noises due to its non-pulsing motion because rotations of its gear are uniform-velocity rotations, its flow is uniform, and its torque is uniform, compared with other gear flow meters. In a gear having relatively a few teeth (the number of teeth Z is 2 to 4) as its gear, the continuous contact tooth profile with which meshing is conducted on the whole surface of the gear tooth profile accompanies no confinement phenomenon, is proper as a tooth profile for a gear of a flow meter, and is variously used in practice.
For example, the tooth profile of a helical-gear positive displacement flowmeter described in Patent Document 1 is a one-point continuous contact tooth profile that employs an involute curve (cutter pressure angle α0≧21.3°) as its reference rack tooth profile, however, the tooth height ratio h in the normal case (in the case of a single curve) is h≈0.665 m (“m” represents “module”) and, even for a combined curve that is formed by connecting the vicinity of a pitch point by a straight line with the cutter pressure angle α0 at the pitch point being α0=15°, the tooth height ratio h is h≈0.724 m. The maximum of the height h0 of the straight line in this case is h0=Z sin2 α0/2.
Therefore, the tooth height ratio of this tooth profile is lower than the tooth height ratio h that is h=π m/4=0.7854 m that is the limit tooth height ratio for the one-point continuous contact tooth profiles and, therefore, no tooth height larger than this can be obtained.
A cycloid tooth profile is characterized in that its specific sliding is constant, but the limit of its tooth height ratio h is h=0.5 m to cause the cutter pressure angle at the pitch point to be zero and to form a one-point continuous contact tooth profile using a single curve. However, although a straight line may be inserted in the vicinity of the pitch point to avoid the cutter pressure angle at the pitch point from being zero, the limit of the tooth height ratio h is h=0.5 m to establish the cycloid tooth profile as a one-point continuous contact tooth profile.
As to an arc tooth profile that is generally called Novikov tooth profile, the largest tooth height ratio h that is h=π m/4=0.7854 m of one-point continuous contact tooth profiles may be obtained when the center of the arc is put at the pitch. However, the tooth height ratio h is h=0.6081 m when the cutter pressure angle α0 at the pitch point is α0=14.5° by shifting the center of the arc because the cutter pressure angle at the pitch point in this case is zero similarly to the case of the cycloid tooth profile. It is also possible to increase the tooth height ratio by inserting a straight line in the vicinity of the pitch point. In this case, the range of the height of the straight line must satisfy a condition that is 0≦h0≦Z sin2 α0/2 and the cutter pressure angle α0 in this case is about α0≧21.5°.
In the above, the height h0 of the straight line is estimated as h0=0.2678 by assuming that the cutter pressure angle α0 of the straight line is α0≧21.5°, satisfies the maximum of the height of the straight line that is h0=0.2686, and the tooth height ratio h in this case is h=0.7303 m. However, the gear tooth profile in this case is a combined-curve tooth profile of an involute and an arc, and the contact type of the arc curve section is not continuous contact but a momentary surface contact.    Patent Document 1: Japanese Patent Publication No. 3310239
However, the standard tooth height ratio (assuming that the total tooth height is 2 h) for an ordinary involute tooth profile is 1.0 m (for a full tooth height) and, therefore, when a tooth profile is used for a gear of a positive displacement flowmeter or of a gear pump, the one with a low tooth height ratio is disadvantageous due to its contact ratio and its discharge amount.
When a positive displacement flowmeter that incorporates therein a pair of helical gears employs an oval pitch curve as its reference rack tooth profile, the tooth height ratio of 0.7854 m that is the theoretical limit for one-point continuous contact tooth profiles may be set. However, no technical idea as above of employing the oval pitch curve as the reference rack tooth profile has been present for the conventional positive displacement flowmeters, and this technical idea has not been realized so far.
The present invention was conceived in view of the above circumstances, and the object thereof is to provide an ideal positive displacement flowmeter that includes a pair of helical gears employing an oval pitch curve as their reference rack tooth profile, is possible to set therein the tooth height ratio of π m/4 (0.7854 m) that is the theoretical limit for one-point continuous contact tooth profiles even for a few teeth, and accompanies no confinement phenomenon and a helical gear.